منابع مشابه
On Integral Operators with Operator-Valued Kernels
It is well known that solutions of inhomogeneous differential and integral equations are represented by integral operators. To investigate the stability of solutions, we often use the continuity of corresponding integral operators in the studied function spaces. For instance, the boundedness of Fourier multiplier operators plays a crucial role in the theory of linear PDE’s, especially in the st...
متن کاملTranslation-invariant bilinear operators with positive kernels
We study L (or Lr,∞) boundedness for bilinear translation-invariant operators with nonnegative kernels acting on functions on R. We prove that if such operators are bounded on some products of Lebesgue spaces, then their kernels must necessarily be integrable functions on R, while via a counterexample we show that the converse statement is not valid. We provide certain necessary and some suffic...
متن کاملWeighted Inequalities for Integral Operators with Some Homogeneous Kernels
In this paper we study integral operators of the form Tf(x) = |x − a1y| −α1 . . . |x − amy| mf(y) dy, α1 + . . . + αm = n. We obtain the L (w) boundedness for them, and a weighted (1, 1) inequality for weights w in Ap satisfying that there exists c > 1 such that w(aix) 6 cw(x) for a.e. x ∈ n , 1 6 i 6 m. Moreover, we prove ‖Tf‖BMO 6 c‖f‖∞ for a wide family of functions f ∈ L( ).
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In this paper Lq → Lp boundedness of integral operator with operator-valued kernels is studied and main result is applied to convolution operators.
متن کاملCommutators of integral operators with variable kernels on Hardy spaces
Abstract. Let TΩ,α (0 ≤ α < n) be the singular and fractional integrals with variable kernel Ω(x,z), and [b,TΩ,α ] be the commutator generated by TΩ,α and a Lipschitz function b. In this paper, the authors study the boundedness of [b,TΩ,α ] on the Hardy spaces, under some assumptions such as the Lr-Dini condition. Similar results and the weak type estimates at the end-point cases are also given...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1965
ISSN: 0022-247X
DOI: 10.1016/0022-247x(65)90008-9